EBK MANUFACTURING ENGINEERING & TECHNOL
7th Edition
ISBN: 9780100793439
Author: KALPAKJIAN
Publisher: YUZU
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Chapter 28, Problem 32QTP
A certain design rule calls for metal lines to be no less than 2-μm wide. If a 1-μm thick metal layer is to be wet etched, what is the minimum photoresist width allowed (assuming that the wet etching is perfectly isotropic)? What would be the minimum photoresist width if a perfectly anisotropic dry-etching process is used?
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Consider the bar, shown in Figure 1 that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.10-3 m², and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
x=0.0
x=2.0
2.0m
10 kN
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x))
-) +1(x) = 0.
d.x
dx
What are the accompanying boundary conditions for this bar?
b) Using the mesh in Figure 2, form the basis functions associated with element 2 and write the FEM
approximation over the element.
1
2
3
1
2
1m
1m
Figure 2: Mesh of 2 elements. Elements are numbered with underlines.
c) The general form of the element stiffness matrix system, with nodes indexed by i and j, is,
AE
Uj
N;(x)l(x)dx
– Ng(0)f(0)
¥ [4]}]{{}}={{{}\(\\+} + {N(2)f(2) = N (0)5() },
(1)
0, respectively.
L
=
(2)
where f(2) and f(0) denote the boundary forces at positions x 2 and x
Evaluate…
answer please
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Question 1
Consider the bar, shown in Figure 1, that undergoes axial displacement due to both a distributed load
and a point force. The bar is of cross-sectional area A = 1.103 m2, and has a modulus of elasticity
E = 100 GPa.
1(x) = 5 kN/m
10 kN
X
x=0.0
x=2.0
2.0m
Figure 1: Bar domain with varying distributed forces.
a) The general form of the governing equations describing the bar's displacement, u(x), is given by,
d
(AE du(x)) + 1(x) = 0.
dx
dx
What are the accompanying boundary conditions for this bar?
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F8
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Chapter 28 Solutions
EBK MANUFACTURING ENGINEERING & TECHNOL
Ch. 28 - Define the terms wafer, chip, die, device,...Ch. 28 - Why is silicon the semiconductor most used in...Ch. 28 - What do the abbreviations BJT, MOSFET, VLSI,...Ch. 28 - Prob. 4RQCh. 28 - Prob. 5RQCh. 28 - What are the purposes of prebaking and...Ch. 28 - Define selectivity and isotropy, and their...Ch. 28 - Prob. 8RQCh. 28 - Prob. 9RQCh. 28 - What are the levels of interconnection?
Ch. 28 - Which is cleaner, a Class-10 or a Class-1 clean...Ch. 28 - Prob. 12RQCh. 28 - What is a via? Why is it important?Ch. 28 - Describe how electrical connections are...Ch. 28 - Prob. 15RQCh. 28 - Prob. 16RQCh. 28 - Comment on your observations regarding the...Ch. 28 - Describe how n-type and p-type dopants differ.Ch. 28 - Prob. 19QLPCh. 28 - How is epitaxy different from other techniques...Ch. 28 - Note that, in a horizontal epitaxial reactor...Ch. 28 - The table that follows describes three...Ch. 28 - Prob. 23QLPCh. 28 - What is accelerated life testing? Why is it...Ch. 28 - Explain the difference between a die, a chip, anda...Ch. 28 - A common problem in ion implantation is...Ch. 28 - Examine the hole profiles shown in Fig. P28.27...Ch. 28 - Referring to Fig. 28.24, sketch the shape of the...Ch. 28 - Prob. 29QTPCh. 28 - Prob. 30QTPCh. 28 - Prob. 31QTPCh. 28 - A certain design rule calls for metal lines to be...Ch. 28 - Prob. 33QTPCh. 28 - If a square mask of side length 100 m is placed on...Ch. 28 - Obtain an expression for the width of the trench...Ch. 28 - Prob. 36SDPCh. 28 - Inspect various electronic and computer equipment,...Ch. 28 - Describe your understanding of the important...Ch. 28 - Make a survey of the necessity for clean rooms in...Ch. 28 - Prob. 40SDPCh. 28 - Prob. 41SDPCh. 28 - Estimate the time required to etch a spur gear...Ch. 28 - Prob. 43SDPCh. 28 - Review the specific devices, shown in Fig. V.2....
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